Fast Radio Bursts (FRBs) are a mysterious flash phenomenon detected in radio wavelengths with a duration of only a few milliseconds, and they may also have prompt gamma-ray flashes. Here we carry out a blind search for msec-duration gamma-ray flashes using the 7-year Fermi Large Area Telescope (Fermi-LAT) all-sky gamma-ray data. About 100 flash candidates are detected, but after removing those associated with bright steady point sources, we find no flash events at high Galactic latitude region (|b|>20 deg). Events at lower latitude regions are consistent with statistical flukes originating from the diffuse gamma-ray background. From these results, we place an upper limit on the GeV gamma-ray to radio flux ratio of FRBs as xi equiv (nu L_nu)_gamma / (nu L_nu)_radio < 10^8, depending on the assumed FRB rate evolution. This limit is comparable with the largest value found for pulsars, though xi of pulsars is distributed in a wide range. We also compare this limit with the spectral energy distribution of the 2004 giant flare of the magnetar SGR 1806-20.
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